Earthquake Nucleation on Faults With Heterogeneous Frictional Properties, Normal Stress

Abstract

AbstractWe examine the development of an instability of fault slip rate. We consider a slip rate and state dependence of fault frictional strength, in which frictional properties and normal stress are functions of position. We pose the problem for a slip rate distribution that diverges quasi‐statically within finite time in a self‐similar fashion. Scenarios of property variations are considered and the corresponding self‐similar solutions found. We focus on variations of coefficients, a and b, respectively, controlling the magnitude of a direct effect on strength due to instantaneous changes in slip rate and of strength evolution due to changes in a state variable. These results readily extend to variations in fault‐normal stress, σ, or the characteristic slip distance for state evolution, Dc. We find that heterogeneous properties lead to a finite number of self‐similar solutions, located about critical points of the distributions: maxima, minima, and between them. We examine the stability of these solutions and find that only a subset is asymptotically stable, occurring at just one of the critical point types. Such stability implies that during instability development, slip rate and state evolution can be attracted to develop in the manner of the self‐similar solution, which is also confirmed by solutions to initial value problems for slip rate and state. A quasi‐static slip rate divergence is ultimately limited by inertia, leading to the nucleation of an outward expanding dynamic rupture: asymptotic stability of self‐similar solutions then implies preferential sites for earthquake nucleation, which are determined by distribution of frictional properties.